Police said in a statement the arrests were made over alleged "active corruption in sports" in an operation code-named Cashball, and officers also searched the premises of one football club and various homes.
It did not identify the club. But local television channels showed police working at Sporting's Alvalade stadium, and sports media said that police suspected some Sporting officials of game-fixing mostly in handball matches but also in some football events, by allegedly bribing referees and players.
One of those detained was Andre Geraldes, the team manager for Sporting and right-hand man of Sporting President Bruno de Carvalho. He has previously dismissed allegations that Sporting may have bribed referees and players. A handball referee was also questioned by police in Porto.
On Tuesday, Sporting condemned "acts of vandalism and aggression" after forward Bas Dost was injured when a group of hooded supporters, armed with sticks and belts, attacked players and staff at the club's training complex.
The club had a tumultuous season, including a spat between de Carvalho and the players over their performance in a Europa League match that culminated in his threat to suspend nearly the entire first-team squad last month.
Police have arrested 21 people after Tuesday's attack.
Portuguese President Marcelo Rebelo de Sousa said the escalation of violence and corruption around sports risked destroying football in the country.
"Faced with the gravity of what happened we have to understand that this climate that has been created over some time... cannot and should not continue, because this escalation will destroy Portuguese football, marring it on the international arena and here inside. It's time to stop the escalation."
In January, prosecutors named the head of football club Benfica, Luis Filipe Vieira, and Vice President Fernando Tavares as suspects in an investigation into a corruption scheme, although Benfica said the probe had nothing to do with the club itself. Benfica is Portugal's most popular club by membership.
(Reporting by Andrei Khalip; Editing by Axel Bugge and Hugh Lawson)
